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Generalized Bregman and Jensen divergences which include some f-divergences

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  • Nishiyama, Tomohiro

Abstract

In this paper, we introduce new classes of divergences by extending the definitions of the Bregman divergence and the skew Jensen divergence. These new divergence classes (g-Bregman divergence and skew g-Jensen divergence) satisfy some properties similar to the Bregman or skew Jensen divergence. We show these g-divergences include divergences which belong to a class of f-divergence (the Hellinger distance, the chi-square divergence and the alpha-divergence in addition to the Kullback-Leibler divergence). Moreover, we derive an inequality between the g-Bregman divergence and the skew g-Jensen divergence and show this inequality is a generalization of Lin's inequality.

Suggested Citation

  • Nishiyama, Tomohiro, 2018. "Generalized Bregman and Jensen divergences which include some f-divergences," OSF Preprints ybmdx_v1, Center for Open Science.
    • Handle: RePEc:osf:osfxxx:ybmdx_v1
    DOI: 10.31219/osf.io/ybmdx_v1
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